Voronoi-Based Curvature and Feature Estimation from Point Clouds

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PCPNet Learning Local Shape Properties from Raw Point Clouds (2017, methodology): “…osculating jets [CP03] based on ﬁtting higher-order primitives robustly, the algebraic point set surface approach based on ﬁtting algebraic spheres [GG07], and approaches based on analyzing the distribution of Voronoi cells in the neighborhood of a point [AB99, ACSTD07, MOG11], among many others.”
Geometric Back-Projection Network for Point Cloud Classification (2019, background): “n drawback is the lack of geometric information compared with well-constructed mesh or volumetric data. In order to acquire more underlying knowledge of point clouds, conventional methods [18], [42], [43] attempted to estimate the geometry of point clouds i.e., face, normals, curvature, etc. In addi”
Eigen-feature analysis of weighted covariance matrices for LiDAR point cloud classification (2014, background): “The Voronoi diagram can be robustly determined for polygonal models or dense and uniformly sampled point clouds, such as the data tested in (Luo et al., 2009; Merigot et al., 2011); however, it is difficult for LiDAR point clouds with inherent noise and incomplete shapes, i.e., missing information.”
Nonasymptotic rates for manifold, tangent space and curvature estimation (2017, background): “Several algorithms have been proposed in that case [24, 6, 21, 17], but with no analysis of their performances from a statistical point of view.”